Abstract
Within the framework of the material point method, a generalized particle in cell method for explicit solid dynamics is presented. In this method, the solids are discretized by finite element meshes, and these meshes are embedded in a background Eulerian grid. The external and internal forces of the solids are calculated on their respective finite element meshes and are mapped to the background grid for solving the momentum equation. Two formulations for computing these forces are presented: one using the original configuration of the solids and the other employs the current configuration. Two and three dimensional numerical examples, covering massive tensile, compressive elastic and plastic deformation, demonstrate that the former formulation performs much better for extremely large deformation problems. Compared with previous material point methods, the proposed method offers these advantages: (i) better representation of solid boundaries, (ii) seamless enforcement of Dirichlet and Neumann boundary conditions, (iii) seamless treatment of material interfaces and (iv) higher efficiency. All of these are achieved with the introduction of a finite element mesh in a supposedly meshfree method.
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